the effects of forming parameters on the single point...

© 2019 IAU, Arak Branch. All rights reserved.

Journal of Solid Mechanics Vol. 11, No. 4 (2019) pp. 825-841

DOI: 10.22034/jsm.2019.668616

The Effects of Forming Parameters on the Single Point Incremental Forming of 1050 Aluminum Alloy Sheet

R. Safdarian *

Department of Mechanical Engineering, Behbahan Khatam Alanbia University of Technology,

Behbahan, Iran

Received 26 July 2019; accepted 28 September 2019

ABSTRACT

The single point incremental forming (SPIF) is one of the dieless forming processes which is widely used in the sheet metal

forming. The correct selection of the SPIF parameters influences

the formability and quality of the product. In the present study,

the Gurson-Tvergaard Needleman (GTN) damage model was

used for the fracture prediction in the numerical simulation of the

SPIF process of aluminum alloy 1050. The GTN parameters of

AA 1050 sheet were firstly identified by the numerical simulation

of tensile test and comparison of the experimental and numerical

stress-strain curves. The identified parameters of the GTN

damage model were used for fracture prediction in the SPIF

process. The numerical results of the fracture position, thickness

variation across the sample and forming height were compared

with the experimental results. The numerical results had good

agreement with the experimental ones. The effect of SPIF main

parameters was investigated on the formability of samples by the

verified numerical model. These parameters were tool rotation

speed, tool feed rate, tool diameter, wall angle of the sample,

vertical pitch, and friction between the tool and the blank.

© 2019 IAU, Arak Branch. All rights reserved.

Keywords: Single point incremental forming (SPIF); GTN damage model; Response surface method (RSM); Fracture; Finite

element method (FEM).

1 INTRODUCTION

INGLE point incremental forming (SPIF) process is one of the dieless sheet metal forming processes are widely studied in the research papers. Because of the capability of the SPIF process to complex shape

manufacturing, this process can be widely used in the automotive and aerospace industries. Bagudanch et al. [1]

studied the effect of the variation of several process parameters in the SPIF. Their results showed that spindle speed

variation was the most significant parameter. Gatea et al. [2] reviewed some of the studies in the technological

______ *Corresponding author. Tel.: +98 61 52721191.

E-mail address: [email protected] (R. Safdarian).

S

R. Safdarian 826

© 2019 IAU, Arak Branch

capabilities and limitations of the SPIF. The effect of process parameters was studied on the formability,

deformation mechanics and springback. Raju et al. [3] used a SPIF experimental setup for forming of multiple

commercially pure aluminum sheets. Their results showed that the sheets failed under the combination of shear and

brittle failure mode. Guzmán et al. [4] used an extended Gurson-Tvergaard-Needleman (GTN) model and finite

element (FE) simulation to predict damage in the SPIF. Their results showed that wrong coalescence modeling in

the GTN model caused the underestimates of failure angle in the SPIF. Dakhli et al. [5] used the experimental tests

of SPIF for forming two geometries of parts with the same process parameters. They studied the effects of straight

and circular generatrix profiles on the forming forces, thickness distribution, shape accuracy and surface roughness

of the formed shape. Their results indicated that using straight generatrix caused a more uniform thickness

distribution in the final part. McAnulty et al. [6] reviewed 35 papers in the field of SPIF and the effect of process

parameters on the formability of the sheet in this process. Results of this study showed that there is a lack of focus

on the parameter interactions in the literature. Bagudanch et al. [7] studied the forming forces in the SPIF of variable

wall angle geometry under different bending conditions. Their results indicated that the maximum forming force

decreased by the spindle speed increase while it was increased by the tool diameter increase. The effect of

temperature and tool rotation speed was studied on the SPIF of titanium alloy by Palumbo and Brandizzi [8]. The

effect of heating by an electrical heater and high tool rotation speed were studied on the formability of Ti6Al4V

blank. Their results indicated that high rotation speed had a positive effect on the formability and increased the level

of stretching. Hadoush and van den Boogaard [9] used a substructuring method for time reduction of implicit

simulations of the SPIF. In this method, the finite element mesh was divided into several non-overlapping parts.

Their results showed that this method was 2.4 faster than the classical implicit method. Duflou et al. [10] used

experimentally multi-step tool path strategy to increase the process window. Their results showed that the

formability increased by the multi-step forming. Gupta and Jeswiet [11] studied the effect of feed rate and tool

rotation speed on the temperature in the SPIF of AA5754-H32. They founded that lubricant and rig design had an

effect on the net heat within the system. Edwards et al. [12] did experimental tests of the SPIF to investigate the

effect of forming parameters on the springback of polycarbonate sheets. Results showed that the springback

decreased by the spindle rotational speed and the feed rate increase. Bansal et al. [13] used an analytical model to

predict the sheet thickness, forming forces and contact area in the SPIF. Predicted results were compared with

experimental ones. Results showed that the presented analytical model required less computational resources

compared to the FE analysis. Behera et al. [14] reviewed some of studies and developments in the SPIF field. The

different aspect of this process like tool path and tooling strategies, failure mechanism, forming mechanics and

estimation of forming force were investigated and provided a roadmap for future of this process. Martins et al. [15]

presented a theoretical analysis of the SPIF. This theoretical model was based on the membrane analysis with bi-

directional in plane contact friction. Martínez-Romero et al. [16] studied the dynamic interaction among the tool, the

sheet and the die during the forming process. Their results showed that a robust experimental setup needed to avoid

undesirable effects of vibration on the final part.

In the present study, the Gurson-Tvergaard Needleman (GTN) damage model was used for the fracture

prediction in the SPIF process of aluminum alloy 1050. Response surface method (RSM) was coupled with the finite

element to identify the GTN parameters of the AA 1050 sheet. For this purpose, different sets of the GTN

parameters were used for simulation of the uniaxial tensile test in the Abaqus/Explicit. Then, the optimum

parameters were selected based on the comparison of the experimental and numerical stress-strain curves. The

identified GTN parameters were used in the numerical simulation of the SPIF process of AA 1050 to produce a

truncated conical geometry. The numerical model of the SPIF was verified with the experimental tests of the present

study. The verified model was used to investigate the effect of the SPIF parameters on the formability, forming

height, and thickness variations in the critical element. These forming parameters were: tool diameter, tool rotation

speed, tool feed rate, vertical pitch, friction between the tool and the blank and wall angle of the sample. The

novelties of the present study are: (1) identification of GTN parameters of AA 1050 sheet using the anti-inference

method and numerical simulation of tensile test based on the RSM design of experiment, (2) investigation of effect

of GTN parameters on the ultimate stress and related strain in the stress-strain curve of AA 1050 sheet, (3)

investigation of effects of main parameters of SPIF on the formability and thinning of AA 1050 sheet using the

experimental tests and numerical simulations.

827 The Effects of Forming Parameters on the Single ….


2 METHODOLOGY

2.1 Material properties

In the present study, the 1050 aluminum alloy sheet with 1 mm thickness was used in the SPIF process. This

aluminum alloy has electrical conductivity, excellent corrosion resistance, and high ductility. Therefore, the AA

1050 is mostly used in the automotive industry, food industry containers, chemical process plant equipment, and

light reflectors. The uniaxial tensile test based on the ASTM standard [17] was used to calculate the mechanical

properties of this aluminum alloy. Fig. 1 shows the true stress-strain curve of the AA 1050 sheet.

Fig.1

True stress-strain curve of AA 1050.

2.2 The experimental setup of the SPIF

In the present study, the square sheet of AA 1050 with the dimension of 200 mm×200mm and the thickness of 1 mm

was used for the SPIF process. As Fig. 2 (a) shows a three-axis CNC milling machine was used for this process and

the G-cod of spiral tool paths was generated using the CAM software Power Mill. The blank was fixed from four

edges in the fixture to avoid any movement. The forming tool was a cylindrical rod of diameter 14 mm with a

hemispherical head which was made of high-speed steel (HSS). The designed part for production in the SPIF is a

truncated cone with a constant wall angle of 30˚ and depth of 66 mm. Fig. 2 (b) shows the designed part in the Solid

Works software. Although the depth of the final part is 66 mm, it maybe reduces by the forming condition variations

such as friction condition between the blank and the forming tool. Two different contact conditions were used

between the forming tool and the blank in the experimental tests of the SPIF. In one set of the experimental tests, the

hydraulic oil was used as a lubricant in the blank and tool contact and another set of experimental tests were done

without lubricant.

(a)

(b)

Fig.2

(a) The experimental setup of the SPIF,. (b) The design truncated cone for experimental and numerical tests.

2.3 Identification of GTN damage parameters

The Gurson–Tvergaard–Needleman (GTN) based on the following equation was used for the fracture prediction in

the SPIF of AA 1050 sheet.

2

221 3

32 1 0

2

eq * *m

y y

qq f .cosh q f

(1)

where m is the mean stress, eq is the Von Mises equivalent stress, y is the yield stress of material, q1, q2

and q3 are tha material parameters.

R. Safdarian 828


The relationship between *f and f is given as follows:

11

c*

cc c f

f c

f f f

f / q ff f f f

f f

(2)

where ff is void volume fraction at total failure and cf is critical void volume fraction. f is the void volume

fraction which is the ratio of total volume of cavities to the volume of the body. The growth of existing voids and

nucleation of new voids cause the increase of total void volume fraction. Therefore, the rate of void volume fraction

can be shown by the following equation:

growth nucleationf f f (3)

The plastic incompressibility of a circumambient matrix of the voids based on the mass balance in representative

volume elements is used to specify the void growth rate.

1 plgrowth kkf f . (4)

where plkk is the plastic hydrostatic strain.

Normal distribution of void nucleation was proposed by [18] using the following equation:

2

1

22

plpl plN N

nucleationNN

ff A exp

SS

(5)

where NS is standard deviation, pl the equivalent plastic strain of the material, N the mean value of the

distribution of plastic strain, Nf the volume fraction of void nucleation.

The coefficients of 0 1 2c N f N Nf , f , f , f , ,S ,q ,q and 2q required to be identified for using the GTN damage

model. The value of GTN parameters related to the materials microstructure is different for each material. Anti-

inference method is one of the methods for calculation of GTN parameters which was used by He et al. [19]. In this

method, the combination of the FE simulation with the experimental tensile test is used and the GTN parameter

identified by the comparison of the numerical and experimental stress-strain curves. In the present study, the initial

values of the GTN parameters for AA 1050 were selected based on the results of Kacem et al. [20]. Table 1., shows

the GTN parameters of Kacem et al. [20].

Table 1

Known parameters of GTN model for AA 1050 [20]

Parameter 1q 2q 3q NS 0f N Nf ff cf

Value 1.5 1 2.25 0.1 0 0.3 0.004 032 0.014

For a better selection of the GTN parameters, a design of experiment (DOE) was done using the Response

Surface Method (RSM) with the technique of Central Composite Design (CCD) and considering the parameters of

Ref. [20]. In this DOE, the maximum numerical stress and numerical strain at the maximum stress of the stress-

strain curve were compared with the experimental ones. The value of q1, q2, q3, f0, and SN was selected as constant in

the numerical simulation using information of Table 1. For other GTN parameters, a range of value was considered

based on the results of Kacem et al. [20]. These parameters were mean 0 1 0 4N. . , effective void volume

fraction 0 002 0 006N. f . , the final void volume fraction 0 2 0 35f. f . and critical void volume fraction

0 005 0 02c. f . . Table 2., shows the list of 31 runs of numerical simulation of tensile test with different

parameters for the GTN model. The stress–strain curve of these numerical simulations were compared with the

experimental results.



Table 2

The DOE of numerical simulation of the tensile test.

Run num. N Nf ff cf

1 0.25 0.004 0.275 0.0125

2 0.1 0.006 0.2 0.005

3 0.25 0.004 0.275 0.0125

4 0.1 0.002 0.35 0.005

5 0.25 0.005 0.275 0.0125

6 0.25 0.004 0.275 0.01625

7 0.175 0.004 0.275 0.0125

8 0.1 0.006 0.35 0.005

9 0.25 0.004 0.2375 0.0125

10 0.25 0.004 0.275 0.0125

11 0.4 0.002 0.35 0.02

12 0.1 0.002 0.2 0.02

13 0.4 0.006 0.35 0.02

14 0.325 0.004 0.275 0.0125

15 0.25 0.004 0.275 0.0125

16 0.4 0.002 0.2 0.02

17 0.25 0.004 0.3125 0.0125

18 0.4 0.006 0.2 0.02

19 0.1 0.006 0.35 0.02

20 0.25 0.003 0.275 0.0125

21 0.25 0.004 0.275 0.0125

22 0.4 0.006 0.2 0.005

23 0.25 0.004 0.275 0.0125

24 0.4 0.002 0.35 0.005

25 0.25 0.004 0.275 0.0125

26 0.25 0.004 0.275 0.00875

27 0.1 0.006 0.2 0.02

28 0.1 0.002 0.35 0.02

29 0.1 0.002 0.2 0.005

30 0.4 0.002 0.2 0.005

31 0.4 0.006 0.35 0.005

Ref. [20] 0.3 0.004 0.32 0.014

2.4 Numerical simulation

In the first part of the numerical simulation, the uniaxial tensile test was modeled based on the experimental test

conditions in the commercially available finite element code Abaqus/Explicit 6.14 to determine the GTN

parameters. Because of symmetry, just half of the uniaxial sample was modeled in the Abaqus. The nine parameters

of the GTN damage model imported into the material properties of numerical simulation and 32 simulations were

done based on Table 2. The void volume fraction (VVF) criterion was used to identify the first damaged element.

When the VVF equaled to the ff , the element started to damage and the stress-strain curve of the damaged element

compared with the experimental one. In the second part of the numerical simulation, the process of the SPIF was

modeled in the Abaqus/Explicit 6.14. This model consists of the AA 1050 blank and the forming tool. Because of

negligible deformation of the forming tool, it was modeled as a rigid body. The AA 1050 blank was modeled as a

deformable part by four nodes Kirchhoff thin shell elements (S4R) with shell thickness equal to the thickness of

R. Safdarian 830


blank (1 mm), five Gaussian integration points through the thickness and dimensions of 200 mm×200 mm. The

blank’s edges fixed by using encastre boundary condition. Fig. 3 shows this model, the boundary conditions, and the

meshed blank. As this figure shows, the fine mesh was used for the blank. The forming tool is a cylindrical rod with

a hemispherical head which touches the blank in the forming process. The tool had rotation speed about its axis and

also moved in three directions. As mentioned in the experimental part, the designed geometry for the SPIF was the

truncated cone with a constant wall angle (Fig. 2).

Fig.3

Numerical model for the SPIF process in the Abaqus/Explicit.

The Solidworks software was used to produce the tool path coordinate which was a helix path. These coordinates

were imported as boundary conditions of the forming tool to the Abaqus. After verification of the SPIF numerical

model with the experimental tests of the present study, this model was used to investigate the effect of forming

parameters on the formability and thickness distribution of AA 1050 blank in the SPIF. The GTN damage model

whose parameters were identified in the previous section used for fracture prediction in the FE simulation of the

SPIF process. The void volume fracture (VVF) criterion was used to predict the position and time of fracture in the

blank. When the VVF equals to the ff , the element starts to damage. The forming parameters and their values have

been shown in Table 3.

Table 3

Forming parameters of the SPIF and their values.

Forming parameters Verification Level 1 Level 2 Level 3

Tool diameters (mm) 14 12 16 18

Tool rotational speed (rpm) 250 100 500 1000

Feed rate (mm/s) 6500 6500 7500 8000

Helix pitch (mm) 0.6 1.2 2 3.5

Wall angle (degree) 30˚ 25˚ 35˚ 45˚ Friction between the tool and sheet 0.4 0.2 0.4 0.8

3 RESULTS

3.1 Identification of GTN parameters

The effect of GTN parameters was studied on the maximum stress and strain at the maximum stress of the stress-

strain curve from the tensile test. The VVF criterion was used for selection of the first element of the sample which

started to fracture in the Abaqus simulations. The stress-strain curve of the first element which it’s VVF = ff was

compared with the experimental one. Table 4., shows the numerical stress, numerical strain, and their error values

compared to the experimental results. As Table 4., shows, the error values of the numerical stress for all simulations

is less than 1 % and this shows that the maximum stress of numerical stress-strain curve is near to the experimental

results and it is not sensitive to the variation of the GTN parameters. This table shows that the numerical strain is

more sensitive to the selected GTN parameters than the numerical stress. The effect of GTN parameters on the error

value of the numerical strain has been shown in Fig. 4. As this figure shows, the error value decreased by the

increase of N and increased by the increase of Nf . The variation of ff and cf didn’t have a significant influence

on the error value of the numerical strain. The minimum error value happened for 0 4N . and 0 002Nf . which

were selected as optimum values for these two parameters of the GTN model. Whereas the variation of two other

parameters of ff and cf didn’t have a significant influence on the error value of the numerical strain, the suggested



values by Kacem et al. [20] were selected as optimum parameters for these parameters. Therefore, the optimum

parameters of the GTN damage model for fracture prediction in the SPIF process of AA 1050 have been

summarized in Table 5.

Table 4

Comparison of numerical and experimental stress and strain.

Run num. Numerical strain Numerical stress Error value of strain (%) Error value of stress (%)

1 0.056893 177.297 9.410 0.730

2 0.057973 177.029 11.486 0.880

3 0.056893 177.297 9.410 0.730

4 0.056678 177.217 8.997 0.775

5 0.057079 177.297 9.767 0.730

6 0.056893 177.297 9.410 0.730

7 0.056531 177.221 8.714 0.772

8 0.057973 177.029 11.486 0.880

9 0.056893 177.297 9.410 0.730

10 0.056893 177.297 9.410 0.730

11 0.0564 177.287 8.461 0.735

12 0.056678 177.217 8.997 0.775

13 0.056392 177.287 8.447 0.735

14 0.056466 177.288 8.589 0.735

15 0.056893 177.297 9.410 0.730

16 0.0564 177.287 8.461 0.735

17 0.056893 177.297 9.410 0.730

18 0.056392 177.287 8.447 0.735

19 0.057973 177.029 11.486 0.880

20 0.056801 177.297 9.232 0.730

21 0.056893 177.297 9.410 0.730

22 0.056392 177.287 8.447 0.735

23 0.056893 177.297 9.410 0.730

24 0.0564 177.287 8.461 0.735

25 0.056893 177.297 9.410 0.730

26 0.056893 177.297 9.410 0.730

27 0.057973 177.029 11.486 0.880

28 0.056678 177.217 8.997 0.775

29 0.056678 177.217 8.997 0.775

30 0.0564 177.287 8.461 0.735

31 0.056392 177.287 8.447 0.735

Ref. [20] 0.056577 177.294 8.801 0.731

Table 5

The optimum parameters of the GTN model for AA 1050.

Parameter 1q 2q 3q NS 0f N Nf ff cf

Value 1.5 1 2.25 0.1 0 0.4 0.004 0.320 0.014

R. Safdarian 832


Fig.4

The effect of GTN parameters on the error value of numerical strain.

3.2 Fracture prediction of the SPIF process by the GTN model

For verification of the SPIF numerical model, some experimental tests were done using the forming parameters of

Table 3., (verification column). These experimental tests were done in two different contact conditions between the

tool and the blank. Because of using oil as a lubricant in the blank and tool contact, one set of the experimental tests

was done in the frictionless condition. The second set of experimental tests of the SPIF was done without any

lubricant between the tool and the blank. The numerical simulations of the SPIF were done in the conditions of the

experimental tests. The GTN damage model with parameters of Table 5., was used for fracture prediction in the

numerical simulations of the SPIF.

The feed rate of 6500mm/s was used for the forming tool in the FEM simulation for CPU time reduction, but the

quasi-static condition of simulation in the Abaqus was investigated by the comparison of the internal and kinetic

energies. The ratio of kinetic energy to internal energy should be less than 5 percent for the quasi-static simulations

in the Abaqus/Explicit [21]. Comparison of the kinetic and the internal energies has been presented in Fig. 5. As this

figure shows, the variation of the kinetic energy is stable and under the internal energy. Therefore, the selected feed

rate for the forming tool was used in all FEM simulation of the SPIF.

Fig.5

Kinetic and internal energy comparison.

Two sets of experimental tests of the SPIF were done for verification of the numerical model and also the GTN

parameters. These experimental tests were done with the process parameters of Table 3. Fig. 6 shows the

comparison of the experimental and numerical samples after the SPIF process with two different contact conditions

between the forming tool and the blank. Fig. 6 (a) shows the numerical and experimental samples with the

frictionless condition were obtained by using oil as a lubricant between the forming tool and the blank in the

experimental tests. The penalty contact with frictionless formulation was used in the Abaqus/Explicit. Fracture

didn’t happen for both numerical and experimental samples in the frictionless condition. As Fig. 6 (a) illustrates the

maximum value of VVF is 0.109922 for the numerical sample which is far from 0 32ff . . Fig. 6 (b) shows the

comparison of the experimental and the numerical samples after the SPIF in the friction condition. For both



numerical and experimental samples fracture happened in the samples wall near the top corner. In the numerical

sample, the VVF = 0 32ff . at fracture time (Fig. 6 (b)). For better comparison of thinning of the experimental and

numerical samples, the thickness variation of both samples in the frictionless condition was extracted along a path

across the samples. This path was selected in the region with minimum thickness (Fig. 7). The thickness variation of

the FEM and the experimental samples has been presented in Fig. 8. As this figure shows, the thickness variation of

the FEM has a good agreement with the experimental results. This figure also shows that the minimum thickness

happens in the samples wall near the bottom corner. Fig. 9 shows the forming height comparison of the numerical

and experimental samples for two different contact conditions of the forming tool and the blank. In the frictionless

and friction condition, the forming height was predicted by the FEM with error values of 0.83% and 3.62%,

respectively. These error values showed that the numerical model had good accuracy for the forming height

prediction.

(a) Frictionless condition

(b) Friction condition Fig.6

Comparison of experimental and numerical samples after the SPIF.

Fig.7

Thickness measuring along a path in the numerical and experimental samples.

Fracture position

Top corner

Path Bottom corner

R. Safdarian 834


Fig.8

Thickness variation comparison for the experimental and numerical samples.

Fig.9

Forming height of the numerical and the experimental samples.

3.3 Effect of the SPIF parameters on the formability

3.3.1 The effect of wall angle of the sample

Four different wall angles of 25°, 30°, 35°, and 45° were selected for the sample in the numerical simulation of the

SPIF. The other forming parameters of the SPIF process were constant and were used from the information of Table

3., (verification column). Fig. 10 shows the four samples which formed with the different wall angle. As this figure

shows just for the sample with the wall angle of 25˚, the VVF= 0 32ff . and the fracture happened in the sample’s

wall near the top corner. The forming height of this sample at fracture time was 27.05 mm. For the other three

samples, the forming height increased by the wall angle increase. The maximum forming height of 60.33 mm

happened for the sample with the wall angle of 45˚ at the minimum value of VVF. The effect of wall angle on the

thickness variation along a path across the samples has been presented in Fig. 11. As this figure shows, the sample

with the wall angle of 25˚ has the lowest level of thickness variation between all samples. The minimum thickness is

0.3 mm which happened for the sample with the wall angle of 25˚ and near the top corner, but it is 0.6 mm for the

sample with the wall angle of 45˚. This figure also shows that the level of thickness variation increase with the wall

angle increase. The element with the maximum VVF was selected and the variations of this parameter in the

simulation time were compared for all the numerical samples. Fig. 12 shows the effect of wall angle of the samples

on the VVF variations. As this figure shows, just for the sample with the wall angle of 25˚ the VVF = 0 32ff . .

This figure shows that the VVF decreases with the wall angle increase.

Friction



(a)

(b)

(c)

(d)

Fig.10

The effect of the sample wall angle of (a) 25˚, (a) 30˚, (a) 35˚and (d) 45˚ on the formability.

Fig.11

The effect of the wall angle of the sample on the thickness

variation across the sample.

Fig.12

The effect of wall angle of the sample on the VVF variation.

3.3.2 The effect of friction between the forming tool and the blank

In the numerical part of this study, the effect of friction between the tool and the blank was investigated by

considering four different friction conditions between the forming tool and the blank. The penalty method was used

to model the contact between the forming tool and the blank. These friction conditions were frictionless, penalty

contact with the friction coefficient of 0.2, 0.4 and 0.8. The other forming parameters of the SPIF process were

selected from the information of Table 3 (verification column). Fig. 13 shows the effect of friction between the

forming tool and the blank on the forming height. As this figure shows, the forming height decreases by the increase

of friction coefficient from 0.2 to 0.8. Fig. 14 shows the effect of different friction conditions on the thickness

variations of the element with the maximum thinning for all the numerical samples. For two samples which formed

Forming height = 27.05mm Forming height = 67.15mm

Forming height = 68 mm Forming height = 60.33 mm

R. Safdarian 836


in the frictionless and friction with the coefficient of 0.2, the minimum thickness was 0.33 mm and 0.29 mm,

respectively. For two other samples which fractured in the SPIF process, the minimum thickness was 0.24 mm. Fig.

15 shows the friction conditions effect on the VVF variations. As this figure shows, for two samples with the friction

coefficient of 0.4 and 0.8 the fracture happens when the VVF = 0.32. Therefore, for the SPIF of AA 1050 with

presented forming parameters, the friction coefficient in the blank and tool contact should be less than 0.2.

Fig.13

The effect of friction between the blank and the tool on the

forming height.

Fig.14

The effect of friction between the tool and the blank on the

thickness variation.

Fig.15

The effect of friction between the tool and blank on the VVF

variation.

3.3.3 The effect of forming tool diameter

The forming tool in the SPIF process was a cylindrical rod with a hemispherical head. The effect of tool diameter

was investigated by considering four different diameters of 12 mm, 14 mm, 16 mm and 18 mm. Fig. 16 shows the

effect of tool diameter on the forming height of AA 1050 blanks in the SPIF process. As this figure shows, the

forming height is fix (67mm) by the tool diameter increase from 12mm to 16mm, but it decreases by the tool

diameter increase to 18mm.

Fig.16

The tool diameter effect on the forming height.



The effect of tool diameter on the thickness variation of the element with the maximum thinning has been

presented in Fig. 17 for different tool diameters. As this figure shows, the minimum thickness increases by the

increase of tool diameter from 12mm to 14mm, but it decreases by the tool diameter increase from 14mm to 18mm.

This phenomenon can be explained by this fact that forming pressure increases in the contact area of the tool and the

blank by the tool diameter decrease and the thickness decreases in this region. By tool diameter increasing from 14

mm to 18 mm the contact area increases between the tool and the blank. The tension and shear stress in the sheet and

tool contact area increases because of the frictionless condition in the tool and blank contact and causes more

deformation in the contact region. Therefore, the thinning increases by the tool diameter increase. Fig. 18 shows the

effect of tool diameter on the VVF variation of the critical elements in the samples which were formed with different

tool diameters. This figure shows that the VVF = 0 32ff . for tool diameter of 18 mm and this sample was

fractured in the forming height of 33.08 mm. The sample which formed using the tool with a diameter of 14 mm had

the minimum value of the VVF and the best formability condition. Because of the frictionless condition, the contact

region of the blank with the tool has more deformation compared to other regions of the blank. This deformation

increased by the tool diameter increasing and finally the fracture happened for the sample which was formed with a

tool diameter of 18 mm.

Fig.17

The effect of tool diameter on the thickness variation.

Fig.18

The effect of tool diameter on the VVF variation.

3.3.4 The effect of tool rotation speed

Tool rotation speed is one of the parameters of the SPIF process whose effect was investigated on the formability of

samples. For this purpose, four different tool rotation speeds of 100, 250, 500 and 1000 rpm were considered for the

forming tool. The other forming parameters were constant and selected from Table 3., (verification column). The

contact of the forming tool and the blank was considered frictionless. The effect of tool rotation speed on the

thickness variation of the critical elements has been shown in Fig. 19. As this figure shows, using the rotation speed

of 250rpm and 1000rpm causes the minimum thickness of 0.32mm and 0.27mm, respectively. Fig. 20 shows the

effect of tool rotation speed on the VVF variations. This figure shows that for all samples the value of VVF didn’t

reach to the 0 32ff . and samples were formed without any fracture, but two samples which formed with the

rotation speed of 250 rpm and 500 rpm had the better condition of formability and thinning.

R. Safdarian 838


Fig.19

The effect of tool rotation speed on the thickness variation.

Fig.20

The effect of tool rotation speed on the VVF variation.

3.3.5 The effect of tool travel speed (feed rate)

Whereas the numerical simulation of the sheet metal forming process should be done in the quasi-static condition in

the Abaqus/Explicit [21], this condition should be considered in the selection of the forming speed (feed rate in the

SPIF process). The ratio of kinetic energy to internal energy should be less than 5 percent for the quasi-static

simulation [21]. Therefore, in the present study, three different feed rates of 6500 mm/s, 7500 mm/s and 8000 mm/s

were selected by considering the quasi-static condition. The other forming parameters were constant and selected

from Table 3. The kinetic and internal energies has been compared in Fig. 5. The effect of feed rate on the thickness

variations of critical elements has been compared in Fig. 21. As this figure shows, the sample which was formed

with the feed rate of 6500 mm/s had the maximum thickness and the thickness decreased by the feed rate increase.

Fig. 22 shows the effect of tool feed rate on the VVF variations. The VVF = ff for the sample which was formed

using the feed rate of 8000 mm/s and it fractured at the forming height of 49.61 mm. For two other samples, the

value of VVF was less than 0 32ff . and fracture didn’t happen in these samples. The sample which was formed

with the feed rate of 6500 mm/s had the minimum level of the VVF.

Fig.21

The effect of tool feed rate on the thickness variation.



Fig.22

The effect of tool feed rate on the VVF variation.

3.3.6 The effect of vertical pitch

The effect of the vertical pitch was investigated on the formability of AA 1050 blank in the SPIF by considering

four values of 0.6 mm, 1.2 mm, 2 mm and 3.5 mm for it. The other forming parameters were constant and selected

from Table 3., (verification column). The frictionless condition was used in the contact of the forming tool and the

blank. Fig. 23 shows the effect of vertical pitch on the thickness variation of the critical element. As this figure

shows, the sample which was formed with the vertical pitch of 1.2 mm had the maximum thickness. The effect of

vertical pitch variation on the VVF has been shown in Fig. 24. Therefore, the formability and the forming height

increased by the vertical pitch increase from 0.6 mm to 1.2 mm. Hirt et al. [22] also resulted that the formability of

the SPIF process improved by the increase of vertical pitch. Whereas the tensile stress increases in the sample wall

with the vertical pitch increase, the forming height decreases by the vertical pitch increase from 1.2 mm to 3.5 mm.

Therefore, the best value for the vertical pitch was 1.2 mm.

Fig.23

The effect of vertical pitch on the thickness variation.

Fig.24

The effect of vertical pitch on the VVF variation.

4 CONCLUSIONS

In the present study, the GTN damage model was used for fracture prediction of AA 1050 sheet in the SPIF process.

Design of experiment coupled with the numerical simulation of the uniaxial tensile test in the Abaqus/Explicit to

identify the parameters of the GTN damage model using the anti-inference method. The effect of GTN parameters

was investigated on the stress-strain curve of the numerical tensile test. Results indicated that the numerical stress-

R. Safdarian 840


strain curve was more sensitive to the N , Nf and variations of two other parameters of ff and cf didn’t

have a significant influence on it.

The identified parameters were used in the numerical simulation of the SPIF process to produce a truncated cone.

The numerical results were compared with the experimental results for two different contact conditions of

frictionless (using oil as a lubricant) and dry contact between the tool and the blank. Results showed that there was a

good agreement between the numerical and the experimental results. The GTN damage model had good accuracy

for prediction of fracture position and the forming height.

The effects of main parameters of the SPIF were investigated on the formability, fracture position, thickness

variation, forming height and the VVF variations by the verified numerical model. The results indicated that the

formability and the forming height increased by the increase of the sample wall angle and fracture happened in the

sample with the wall angle of 25˚. The formability and the forming height decreased by the increase of the tool feed

rate and the friction coefficient in the forming tool and the blank contact. The best parameters were the frictionless

contact and the feed rate of 6500 mm/s. Results showed that the tool rotation speed didn’t have a significant

influence on the formability of AA1050 in the SPIF. The samples’ formability increased by the tool diameter

increase from 12 mm to 14 mm and decreased by increasing from 14 mm to 18 mm. Results indicated that the

forming height increased by the vertical pitch increasing from 0.6 mm to 1.2 mm and it was vice versa by increasing

from 1.2 mm to 3.5 mm. Therefore, the tool diameter of 14 mm and the vertical pitch of 1.2 mm were the best

parameters for the SPIF of AA 1050.

REFERENCES

[1] Bagudanch I., Garcia-Romeu M.L., Ferrer I., Lupiañez J., 2013, The effect of process parameters on the energy consumption in single point incremental forming, Procedia Engineering 63: 346-353.

[2] Gatea S., Ou H., McCartney G., 2016, Review on the influence of process parameters in incremental sheet forming, The International Journal of Advanced Manufacturing Technology 87(1): 479-499.

[3] Raju C., Haloi N., Sathiya Narayanan C., 2017, Strain distribution and failure mode in single point incremental forming (SPIF) of multiple commercially pure aluminum sheets, Journal of Manufacturing Processes 30: 328-335.

[4] Guzmán C.F., Yuan S., Duchêne L., Saavedra Flores E.I., Habraken A.M., 2018, Damage prediction in single point incremental forming using an extended Gurson model, International Journal of Solids and Structures 151: 45-56.

[5] Dakhli M., Boulila A., Tourki Z., 2017, Effect of generatrix profile on single-point incremental forming parameters,The International Journal of Advanced Manufacturing Technology 93(5): 2505-2516.

[6] McAnulty T., Jeswiet J., Doolan M., Formability in single point incremental forming: A comparative analysis of the state of the art, CIRP Journal of Manufacturing Science and Technology 16: 43-54.

[7] Bagudanch I., Centeno G., Vallellano C., Garcia-Romeu M.L., 2013, Forming force in single point incremental forming under different bending conditions, Procedia Engineering 63: 354-360.

[8] Palumbo G., Brandizzi M., 2012, Experimental investigations on the single point incremental forming of a titanium alloy component combining static heating with high tool rotation speed, Materials & Design 40: 43-51.

[9] Hadoush A., van den Boogaard A.H., 2009, Substructuring in the implicit simulation of single point incremental sheet forming, International Journal of Material Forming 2(3): 181-189.

[10] Duflou J.R., Verbert J., Belkassem B., Gu J., Sol H., Henrard C., Habraken A.M., Process window enhancement for single point incremental forming through multi-step toolpaths, CIRP Annals 57(1): 253-256.

[11] Gupta P., Jeswiet J., 2017, Observations on heat generated in single point incremental forming, Procedia Engineering 183:161-167.

[12] Edwards W.L., Grimm T.J., Ragai I., Roth J.T., Optimum process parameters for springback reduction of single point incrementally formed polycarbonate, Procedia Manufacturing 10: 329-338.

[13] Bansal A., Lingam R., Yadav S.K., Venkata Reddy N., 2017, Prediction of forming forces in single point incremental forming, Journal of Manufacturing Processes 28: 486-493.

[14] Behera A.K., de Sousa R.A., Ingarao G., Oleksik V., 2017, Single point incremental forming: An assessment of the progress and technology trends from 2005 to 2015, Journal of Manufacturing Processes 27: 37-62.

[15] Martins P.A.F., Bay N., Skjoedt M., Silva M.B., 2008, Theory of single point incremental forming, CIRP Annals 57(1): 247-252.

[16] Martínez-Romero O., García-Romeu M.L., Olvera-Trejo D., Bagudanch I., Elías-Zúñiga A., 2014, Tool dynamics during single point incremental forming process, Procedia Engineering 81: 2286-2291.

[17] (ASTM) ASfTaM, Metals Test Methods and Analytical Procedures, 1999: 78-98, 501-508. [18] Chu C.C., Needleman A., 1980, Void nucleation effects in biaxially stretched sheets, Journal of Engineering Materials

and Technology 102(3): 249-256.

[19] He M., Li F., Wang Z., 2011, Forming limit stress diagram prediction of aluminum alloy 5052 based on GTN model parameters determined by in situ tensile test, Chinese Journal of Aeronautics 24(3): 378-386.



[20] Kacem A., Jégat A., Krichen A., Manach P.Y., 2013, Forming limits in the hole-flanging process by coupled and uncoupled damage models, AIP Conference Proceedings 1567(1): 575-578.

[21] Hibbitt K., Sorensen, 2002, ABAQUS/CAE User's Manual, Incorporated. [22] Hirt G., Ames J., Bambach M., Kopp R., 2004, Forming strategies and process modelling for CNC incremental sheet

forming, CIRP Annals 53(1): 203-206.

the effects of forming parameters on the single point...

Documents